A bottle of water is found to contain 55 milligrams per liter of calcium. What is this value in grams per liter?
This problem gave us the amount of calcium in units of milligrams per liter of water. Milli- is a prefix, which changes the magnitude of the base unit, which in this case is grams. Each prefix has a corresponding multiplication factor that tells us the magnitude of that prefix. The multiplication factors can also be used to help us convert between different prefixes.
This problem would like us to convert our units from milligrams to grams. So we’re converting milligrams into the base unit, since grams are the base unit for mass. The simplest way to accomplish this is to multiply by the multiplication factor, which would give us 0.055 grams. But it’s often more useful to do conversions using an equivalency that we can get from the multiplication factor. The multiplication factor for milligrams tells us that one milligram is equal to 0.001 grams. We could also multiply both sides of this equivalency by 1000 to get an expression that doesn’t have so many decimal places. Or we can create an expression using the power of 10 that corresponds to the multiplication factor. All of these expressions that tell us how two different units are equal to each other are called conversion factors. We can use these conversion factors to help us convert between these two units.
Let’s see how we can use these conversion factors to help us convert from milligrams per liter into grams per liter. The first thing that we will need to do is express the conversion factor as a fraction. Let’s use this conversion factor. 1000 milligrams is equal to one gram. This is how we would express this conversion factor as a fraction: 1000 milligrams over one gram.
To convert our units, we will multiply by this conversion factor. When the units we want to convert are in the numerator, we need to make sure those same units are in the denominator of the conversion factor so that the units will cancel and we’ll end up with our desired units of grams per liter. If we try to do things the other way around, we wouldn’t get an answer that made much sense. We can use any of the other conversion factors to convert our units as well, which will give us the same answer as long as we’ve made sure we’ve set up the fraction so that the units we want to convert cancel.
So we have found that the 55 milligrams per liter of calcium that was in the bottle of water is equal to 0.055 grams per liter.